Year 5: Tenths, hundredths and thousandths
Part of the Year 5 decimals and percentages chapter. Chapter overview · whole chapter on one page
Tenths, hundredths and thousandths
A decimal is a fraction written with a point. The first digit after the point is in the tenths column, the second is in the hundredths column and the third is in the thousandths column. Each column is ten times smaller than the one on its left.
A hundredth is one of 100 equal parts. The square below has 36 parts shaded, so it shows 0.36, which is 36/100. In its simplest form, 36/100 is 9/25.
A thousandth is one of 1,000 equal parts. The number 0.047 has 0 tenths, 4 hundredths and 7 thousandths. So 0.047 is 47/1,000. The place-value chart shows where each digit goes.
Key ideas
- A decimal is a fraction. Count the decimal places to find the bottom number: 1 place = tenths (10), 2 places = hundredths (100), 3 places = thousandths (1,000).
- Write the digits after the point over the place value, then simplify if you can.
- Adding a zero at the end does not change the value: 0.5 = 0.50 = 0.500 = 5/10 = 50/100 = 500/1,000.
- A whole part stays in front: 3.25 is 3 and 25/100, which is 3 1/4.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.0.36: the digits after the point are 36
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.36⁄100
- Simplify the fraction. The highest common factor (HCF) of 36 and 100 is 4. Divide the top and the bottom by 4.36⁄100 = 9⁄25
- Write the answer. This is the answer.9⁄25
Check. 36 ÷ 100 = 0.36, so 0.36 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the thousandths column, so the bottom number is 1,000.0.047: the digits after the point are 047
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.47⁄1000
- Write the answer. This is the answer.47⁄1000
Check. 47 ÷ 1,000 = 0.047, so 0.047 is right. ✓
Watch out. Count the decimal places: 3 places means a bottom number of 1,000. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.3.25: the digits after the point are 25
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.3 and 25⁄100
- Simplify the fraction. The highest common factor (HCF) of 25 and 100 is 25. Divide the top and the bottom by 25.25⁄100 = 1⁄4
- Write the answer. Read the whole number and the fraction together.3 1⁄4
Check. 25 ÷ 100 = 0.25, so 3.25 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Watch out
Do not write 0.07 as 7/10. The 7 is in the hundredths column, so it is 7/100. The number of decimal places tells you the bottom number, not the number of digits.Exercise 7A Decimals as fractions
Non-calculatorKey words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.0.7: the digits after the point are 7
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.7⁄10
- Write the answer. This is the answer.7⁄10
Check. 7 ÷ 10 = 0.7, so 0.7 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.0.3: the digits after the point are 3
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.3⁄10
- Write the answer. This is the answer.3⁄10
Check. 3 ÷ 10 = 0.3, so 0.3 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.0.09: the digits after the point are 09
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.9⁄100
- Write the answer. This is the answer.9⁄100
Check. 9 ÷ 100 = 0.09, so 0.09 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.0.07: the digits after the point are 07
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.7⁄100
- Write the answer. This is the answer.7⁄100
Check. 7 ÷ 100 = 0.07, so 0.07 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.0.5: the digits after the point are 5
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.5⁄10
- Simplify the fraction. The highest common factor (HCF) of 5 and 10 is 5. Divide the top and the bottom by 5.5⁄10 = 1⁄2
- Write the answer. This is the answer.1⁄2
Check. 5 ÷ 10 = 0.5, so 0.5 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.0.4: the digits after the point are 4
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.4⁄10
- Simplify the fraction. The highest common factor (HCF) of 4 and 10 is 2. Divide the top and the bottom by 2.4⁄10 = 2⁄5
- Write the answer. This is the answer.2⁄5
Check. 4 ÷ 10 = 0.4, so 0.4 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.0.25: the digits after the point are 25
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.25⁄100
- Simplify the fraction. The highest common factor (HCF) of 25 and 100 is 25. Divide the top and the bottom by 25.25⁄100 = 1⁄4
- Write the answer. This is the answer.1⁄4
Check. 25 ÷ 100 = 0.25, so 0.25 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.0.75: the digits after the point are 75
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.75⁄100
- Simplify the fraction. The highest common factor (HCF) of 75 and 100 is 25. Divide the top and the bottom by 25.75⁄100 = 3⁄4
- Write the answer. This is the answer.3⁄4
Check. 75 ÷ 100 = 0.75, so 0.75 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.0.8: the digits after the point are 8
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.8⁄10
- Simplify the fraction. The highest common factor (HCF) of 8 and 10 is 2. Divide the top and the bottom by 2.8⁄10 = 4⁄5
- Write the answer. This is the answer.4⁄5
Check. 8 ÷ 10 = 0.8, so 0.8 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the thousandths column, so the bottom number is 1,000.0.017: the digits after the point are 017
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.17⁄1000
- Write the answer. This is the answer.17⁄1000
Check. 17 ÷ 1,000 = 0.017, so 0.017 is right. ✓
Watch out. Count the decimal places: 3 places means a bottom number of 1,000. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the thousandths column, so the bottom number is 1,000.0.903: the digits after the point are 903
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.903⁄1000
- Write the answer. This is the answer.903⁄1000
Check. 903 ÷ 1,000 = 0.903, so 0.903 is right. ✓
Watch out. Count the decimal places: 3 places means a bottom number of 1,000. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the thousandths column, so the bottom number is 1,000.0.045: the digits after the point are 045
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.45⁄1000
- Simplify the fraction. The highest common factor (HCF) of 45 and 1,000 is 5. Divide the top and the bottom by 5.45⁄1000 = 9⁄200
- Write the answer. This is the answer.9⁄200
Check. 45 ÷ 1,000 = 0.045, so 0.045 is right. ✓
Watch out. Count the decimal places: 3 places means a bottom number of 1,000. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.2.6: the digits after the point are 6
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.2 and 6⁄10
- Simplify the fraction. The highest common factor (HCF) of 6 and 10 is 2. Divide the top and the bottom by 2.6⁄10 = 3⁄5
- Write the answer. Read the whole number and the fraction together.2 3⁄5
Check. 6 ÷ 10 = 0.6, so 2.6 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the hundredths column, so the bottom number is 100.4.25: the digits after the point are 25
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.4 and 25⁄100
- Simplify the fraction. The highest common factor (HCF) of 25 and 100 is 25. Divide the top and the bottom by 25.25⁄100 = 1⁄4
- Write the answer. Read the whole number and the fraction together.4 1⁄4
Check. 25 ÷ 100 = 0.25, so 4.25 is right. ✓
Watch out. Count the decimal places: 2 places means a bottom number of 100. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the thousandths column, so the bottom number is 1,000.1.125: the digits after the point are 125
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.1 and 125⁄1000
- Simplify the fraction. The highest common factor (HCF) of 125 and 1,000 is 125. Divide the top and the bottom by 125.125⁄1000 = 1⁄8
- Write the answer. Read the whole number and the fraction together.1 1⁄8
Check. 125 ÷ 1,000 = 0.125, so 1.125 is right. ✓
Watch out. Count the decimal places: 3 places means a bottom number of 1,000. Do not forget the zeros.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Look at the bottom number. 10 is a power of ten, so the last digit has a clear place value.3⁄10
- Write the decimal point. The bottom number has 1 zero, so the last digit is in the tenths column. Fill the empty places with zeros.0.3
- Write the answer. 0.3
Check. 3 ÷ 10 = 0.3. ✓
Watch out. The bottom number shows where the last digit goes: 10 means tenths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Look at the bottom number. 100 is a power of ten, so the last digit has a clear place value.7⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.0.07
- Write the answer. 0.07
Check. 7 ÷ 100 = 0.07. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Look at the bottom number. 1,000 is a power of ten, so the last digit has a clear place value.9⁄1000
- Write the decimal point. The bottom number has 3 zeros, so the last digit is in the thousandths column. Fill the empty places with zeros.0.009
- Write the answer. 0.009
Check. 9 ÷ 1000 = 0.009. ✓
Watch out. The bottom number shows where the last digit goes: 1,000 means thousandths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Look at the bottom number. 100 is a power of ten, so the last digit has a clear place value.53⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.0.53
- Write the answer. 0.53
Check. 53 ÷ 100 = 0.53. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 4 × 25 = 100, so multiply the top and the bottom by 25.3⁄4 = 75⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.0.75
- Write the answer. 0.75
Check. 3 ÷ 4 = 0.75. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 20 × 5 = 100, so multiply the top and the bottom by 5.9⁄20 = 45⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.0.45
- Write the answer. 0.45
Check. 9 ÷ 20 = 0.45. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 25 × 4 = 100, so multiply the top and the bottom by 4.1⁄25 = 4⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.0.04
- Write the answer. 0.04
Check. 1 ÷ 25 = 0.04. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Look at the bottom number. 10 is a power of ten, so the last digit has a clear place value.6⁄10
- Write the decimal point. The bottom number has 1 zero, so the last digit is in the tenths column. Fill the empty places with zeros.4 + 0.6
- Add the whole number. Put the whole number in front of the decimal point.4 + 0.6 = 4.6
- Write the answer. 4.6
Check. 6 ÷ 10 = 0.6, so 4 + 0.6 = 4.6. ✓
Watch out. The bottom number shows where the last digit goes: 10 means tenths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Look at the bottom number. 100 is a power of ten, so the last digit has a clear place value.7⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.2 + 0.07
- Add the whole number. Put the whole number in front of the decimal point.2 + 0.07 = 2.07
- Write the answer. 2.07
Check. 7 ÷ 100 = 0.07, so 2 + 0.07 = 2.07. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 4 × 25 = 100, so multiply the top and the bottom by 25.3⁄4 = 75⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.10 + 0.75
- Add the whole number. Put the whole number in front of the decimal point.10 + 0.75 = 10.75
- Write the answer. 10.75
Check. 3 ÷ 4 = 0.75, so 10 + 0.75 = 10.75. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write the digits as the top number and the place value as the bottom number. Then simplify.
- Read the digits after the point. The last digit is in the tenths column, so the bottom number is 10.0.8: the digits after the point are 8
- Write the digits over the place value. The top number is the digits. The bottom number is the place value of the last digit.8⁄10
- Simplify the fraction. The highest common factor (HCF) of 8 and 10 is 2. Divide the top and the bottom by 2.8⁄10 = 4⁄5
- Write the answer. This is the answer.4⁄5
Check. 8 ÷ 10 = 0.8, so 0.8 is right. ✓
Watch out. Count the decimal places: 1 place means a bottom number of 10. Do not forget the zeros.
Key words. A fraction has a numerator (the top number) and a denominator (the bottom number). Multiplying the top and the bottom by the same number makes an equivalent fraction.
Method. Multiply the top and the bottom by the same number.
- Compare the bottom numbers. What do we multiply 10 by to get 100? The answer is 10.10 × 10 = 100
- Do the same to the top number. Multiplying the top and the bottom by the same number keeps the fraction the same.4 × 10 = 40
- Write the answer. 40⁄100
Check. 40⁄100 and 4⁄10 both equal 0.4. ✓
Watch out. Multiply the top AND the bottom. Adding the same number to both changes the fraction.
Key words. A fraction has a numerator (the top number) and a denominator (the bottom number). Multiplying the top and the bottom by the same number makes an equivalent fraction.
Method. Multiply the top and the bottom by the same number.
- Compare the bottom numbers. What do we multiply 10 by to get 1000? The answer is 100.10 × 100 = 1000
- Do the same to the top number. Multiplying the top and the bottom by the same number keeps the fraction the same.4 × 100 = 400
- Write the answer. 400⁄1000
Check. 400⁄1000 and 4⁄10 both equal 0.4. ✓
Watch out. Multiply the top AND the bottom. Adding the same number to both changes the fraction.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write 0.4 as a fraction with the bottom number 100, then compare it with Amir’s fraction.
- Write 0.4 as a fraction. The 4 is in the tenths column.4⁄10
- Write it over 100. Multiply the top and the bottom by 10.4⁄10 = 40⁄100
- Compare with Amir’s fraction. Amir’s fraction is ten times smaller than the correct one.4⁄100 ≠ 40⁄100
- Write the answer. No. 0.4 is 40/100, which is 4/10, not 4/100.
Check. 40/100 = 0.4, but 4/100 = 0.04. ✓
Watch out. Count the decimal places: 0.4 has one place, so it is tenths (10), not hundredths.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write each one as a decimal. Three of them are equal to 0.5.
- Write each as a decimal. Divide the top by the bottom, or count the decimal places.0.5 5/10 = 0.5 50/100 = 0.5 5/100 = 0.05
- Find the one that is different. Three of them are five tenths, so the odd one has a different value.5/100 = 0.05, which is ten times smaller than 0.5
- Write the answer. 5⁄100 is the odd one out.
Check. 5 ÷ 100 = 0.05, which is not 0.5. ✓
Watch out. The bottom number decides the place value. 5/100 is hundredths, but 5/10 is tenths.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Write both numbers as thousandths, then compare the top numbers.
- Write 0.125 as thousandths. The 5 is in the thousandths column, so the bottom number is 1,000.125⁄1000
- Write 0.2 as thousandths. Multiply the top and the bottom by 100.2⁄10 = 200⁄1000
- Compare the tops. The bottom numbers are now the same.200 > 125, so 0.2 is bigger.
- Write the answer. No. 0.2 is bigger than 0.125.
Check. 0.2 = 0.200 and 0.125 is smaller. ✓
Watch out. Do not compare 125 and 2 as whole numbers. Compare the place values.