Year 4 Tenths, Hundredths and Money: check-up and SATs-style questions

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Count the tenths that are shaded. Tenths are the first column after the decimal point.

1. Count the equal parts in the whole. The whole is cut into 10 equal parts. Each part is one tenth.
   There are 10 parts, so the bottom number is 10.
2. Count the shaded parts. This gives the top number.
   6 parts are shaded, so the fraction is 610.
3. Write it as a decimal. Tenths go in the first column after the decimal point.

   	ones		tenths
   0.6	0	.	6

   
   0 ones and 6 tenths = 0.6

Check. Go back to a fraction: 0.6 has 6 in the tenths column, so it is 610. ✓

Watch out. Write the 0 ones before the decimal point: 0.7, not .7.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Look at the bottom number: 10 means tenths and 100 means hundredths. Put the digits in a place-value table and write the decimal point after the ones.

1. Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
   7100 is 7 hundredths.
2. Notice there are no tenths. 7 hundredths is less than 1 tenth (1 tenth = 10 hundredths). The tenths column must hold a 0.
   0 tenths and 7 hundredths
3. Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.

   	ones		tenths	hundredths
   0.07	0	.	0	7

4. Write the decimal.
   7100 = 0.07

Check. Go back to a fraction: 0.07 = 7100. ✓

Watch out. 7 hundredths is 0.07, not 0.7. The 0 in the tenths column keeps the 7 in the hundredths column.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   75 hundredths = 75100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   75 and 100 both divide by 25.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   75 ÷ 25 = 3 and 100 ÷ 25 = 4
   75100 = 34
4. Write the fraction.
   0.75 = 34

Check. Go back to a decimal: 34 of 100 is 75, which is 75 hundredths = 0.75. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. Place value means that a digit is worth different amounts in different columns. After the decimal point the columns are tenths (0.1) and hundredths (0.01).

Method. Find which column the digit is in. The value is the digit times the value of that column.

1. Write the number in a place-value table. This shows which column each digit is in.

   	ones		tenths	hundredths
   5.38	5	.	3	8

2. Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.
   The digit 3 is in the tenths column.
3. Work out its value. One tenth is worth 0.1. The digit tells us how many of them there are.
   3 × 0.1 = 0.3
4. Write the answer.
   3 tenths (0.3)

Check. Check by adding up all the parts: they should make 5.38. ✓

Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
   0 ones
4. Write the answer. Put the decimal point after the ones.
   56 ÷ 100 = 0.56

Check. Go the other way: 0.56 × 100 = 56. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.

Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.

1. Write the numbers in a place-value table. Line up the decimal points.

   	ones		tenths	hundredths
   0.61	0	.	6	1
   0.16	0	.	1	6
   0.66	0	.	6	6

2. Compare the columns from the left. Where the digits are the same, look at the next column to the right.
   Ones: 0.61 has 0, 0.16 has 0, 0.66 has 0. All the same, so look at the next column.
   Tenths: 0.61 has 6, 0.16 has 1, 0.66 has 6. Smallest to biggest: 1, 6.
   Hundredths: 0.61 has 1, 0.66 has 6. Smallest to biggest: 1, 6.
3. Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.
   0.16,  0.61,  0.66

Check. Count them: 3 numbers in the question and 3 in the answer. ✓

Watch out. Do not forget a number. Tick each one off as you write it.

Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.

Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two whole numbers that 6.7 is between. Rounding to the nearest whole number means choosing the closest whole number.
   6  <  6.7  <  7
2. Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.
   The tenths digit is 7.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)
   7 is 5 or more, so round up.
4. Write the answer.
   6.7 ≈ 7 (to the nearest whole number)

Check. Distances: 6.7 − 6 = 0.7 and 7 − 6.7 = 0.3. 7 is the nearer whole number. ✓

Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Divide the pence by 100 to find the pounds. The pence left over go after the decimal point, with two digits.

1. Remember: 100 pence make 1 pound. So we divide the pence by 100 to find the pounds.
   605 ÷ 100 = 6 remainder 5
2. Write the pounds and the pence. 6 pounds and 5p.
   6 pounds and 5p
3. Put them together with a decimal point. The pence always get TWO digits: write a 0 in front if there is only one.
   £6.05   (the 0 holds the tens-of-pence place)

Check. Go back: £6.05 = 6 × 100 + 5 = 605p. ✓

Watch out. Do not write £6.5: money always has two digits after the point.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.

1. Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
2. Step 1: find the change. Take the cost away from the money paid.
   £10.00 − £3.85 = £6.15
   

   	£10	£1		10p	1p
   £	01	90	.	90	100
   − £		3	.	8	5
   £		6	.	1	5

3. Write the answer.
   The change is £6.15

Check. Add the change to the cost: £3.85 + £6.15 = £10.00, the money paid. ✓

Watch out. Take the cost away from the money paid, not the other way round.

Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.

Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.

1. Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.
   3.5 = 3.50
2. Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.

   	O		t	h
   	3	.	5	0
   −	1	.	7	5
   		.

3. Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
   0 is not enough to take away 5. We need to exchange.
   Exchange 1 from the tenths column: 5 becomes 4, and the hundredths column goes from 0 to 10.
   10 − 5 = 5
4. Exchange, then subtract the tenths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.
   4 is not enough to take away 7. We need to exchange.
   (There were 5 in this column to start with, but we gave one away in an earlier exchange.)
   Exchange 1 from the ones column: 3 becomes 2, and the tenths column goes from 4 to 14. (This crosses the decimal point.)
   14 − 7 = 7
5. Subtract the ones. Now the next column to the left.
   (This digit is 2 now, not 3, because we exchanged from this column.)
   2 − 1 = 1
6. Read the answer. Put the decimal point in the answer, directly under the other decimal points.

   	O		t	h
   	23	.	145	100
   −	1	.	7	5
   	1	.	7	5

   
   3.50 m − 1.75 m = 1.75 m

Check. Add back: 1.75 m + 1.75 m = 3.50 m. ✓

Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. A hundred square has 100 small squares. Each is one hundredth. Count the shaded squares, then write the decimal.

1. Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.
   10 × 10 = 100 squares
2. Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.
   3 full rows = 30 squares
   30 + 6 = 36 squares
3. Write the fraction. The top number is the shaded squares.
   36100
4. Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.

   	ones		tenths	hundredths
   0.36	0	.	3	6

   
   36 hundredths = 0 ones, 3 tenths and 6 hundredths, so 0.36

Check. Go back: 0.36 is 36100. ✓

Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 10 moves each digit 1 place to the right in the place-value chart.

1. Write the number in a place-value chart. Dividing by 10 makes every digit 10 times smaller.
2. Move every digit 1 column to the right. Each digit slides one column to the right, to a column that is worth 10 times less.
3. Write the answer. Put the decimal point after the ones.
   84 ÷ 10 = 8.4

Check. Go the other way: 8.4 × 10 = 84. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Key words. Place value means that a digit is worth different amounts in different columns. After the decimal point the columns are tenths (0.1) and hundredths (0.01).

Method. Find which column the digit is in. The value is the digit times the value of that column.

1. Write the number in a place-value table. This shows which column each digit is in.

   	ones		tenths	hundredths
   6.72	6	.	7	2

2. Find the column the digit is in. The columns, from the left, are tens, ones, then after the decimal point tenths and hundredths.
   The digit 7 is in the tenths column.
3. Work out its value. One tenth is worth 0.1. The digit tells us how many of them there are.
   7 × 0.1 = 0.7
4. Write the answer.
   7 tenths (0.7)

Check. Check by adding up all the parts: they should make 6.72. ✓

Watch out. The 0.5 in a number like 3.52 is worth 5 tenths (0.5), not 5 ones.

Key words. To round a number to the nearest whole number is to change it to the whole number that is closest to it. ≈ means “is about equal to”.

Method. Look at the tenths digit (just after the decimal point). If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two whole numbers that 12.6 is between. Rounding to the nearest whole number means choosing the closest whole number.
   12  <  12.6  <  13
2. Look at the tenths digit. It is the digit just after the decimal point. It tells us if we are past halfway.
   The tenths digit is 6.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down. (Halfway, like 0.5, rounds up.)
   6 is 5 or more, so round up.
4. Write the answer.
   12.6 ≈ 13 (to the nearest whole number)

Check. Distances: 12.6 − 12 = 0.6 and 13 − 12.6 = 0.4. 13 is the nearer whole number. ✓

Watch out. Only the tenths digit decides. A number like 3.49 rounds down, even though 9 is big: look at the first digit after the point only.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write each one as a decimal or a fraction and compare it with one half, which is 0.5.

1. Write 1/2 as a decimal. A half is 5 tenths, or 50 hundredths.
   12 = 0.5
2. Check each option.
   A: 0.5 is a half ✓
   B: 0.05 is 5 hundredths, not a half
   C: 510 is 5 tenths, which is a half ✓
   D: 0.25 is a quarter, not a half
3. Choose the two.
   A and C

Check. A half of 100 squares is 50 squares, which is 0.5 or 5 tenths. ✓

Watch out. 0.5 and 0.05 are different numbers.

Key words. To order numbers is to put them in a list. Ascending means smallest first. Descending means biggest first.

Method. Write the numbers in a place-value table and compare the digits column by column, starting from the left. Then list them smallest first.

1. Write the numbers in a place-value table. Line up the decimal points.

   	ones		tenths	hundredths
   4.35	4	.	3	5
   4.53	4	.	5	3
   4.05	4	.	0	5

2. Compare the columns from the left. Where the digits are the same, look at the next column to the right.
   Ones: 4.35 has 4, 4.53 has 4, 4.05 has 4. All the same, so look at the next column.
   Tenths: 4.35 has 3, 4.53 has 5, 4.05 has 0. Smallest to biggest: 0, 3, 5.
3. Write them smallest first. Write the ORIGINAL numbers and check that you have used every one.
   4.05,  4.35,  4.53

Check. Count them: 3 numbers in the question and 3 in the answer. ✓

Watch out. Do not forget a number. Tick each one off as you write it.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Multiply the pounds by 100 and add the pence.

1. Remember: 1 pound is 100 pence. So we multiply the pounds by 100.
   6 × 100 = 600p
2. Add the pence. The two digits after the decimal point are the pence.
   600p + 5p = 605p
3. Write the answer with the unit p. Pence are written with a small p after the number.
   £6.05 = 605p

Check. Go back: 605p ÷ 100 = £6.05. ✓

Watch out. £6.05 is 605p, not 65p: if the pence are less than 10, put a 0 in: £6.05 = 605p.

Key words. To compare numbers is to say which is bigger. < means “is less than” and > means “is greater than”.

Method. Compare the numbers column by column from the left, not as whole numbers. Give them the same number of decimal places first.

1. Look at what Aisha did. Aisha compared 65 and 7 as if they were whole numbers.
   65 > 7, so Aisha thinks 0.65 > 0.7
2. Give both numbers the same number of decimal places. Adding a 0 on the end does not change the value.
   0.7 = 0.70
3. Compare them in a place-value table. Look at the tenths first.

   	ones		tenths	hundredths
   0.65	0	.	6	5
   0.70	0	.	7	0

4. Decide who is right.
   0.65 < 0.7. Aisha is wrong.

Check. On a number line, 0.7 = 0.70 is to the right of 0.65. ✓

Watch out. A decimal with more digits is not always bigger. Compare tenths first, then hundredths.

Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.

Method. Find the cost of each group of items. Add them to find the total. Then take the total away from the money paid to find the change.

1. Find the cost of 3 apples. 3 lots of £0.45.
   3 × £0.45 = £1.35  (45p × 3 = 135p)
2. Add the costs to find the total. Use a column method, with the decimal points lined up.
   £1.35 + £1.20 = £2.55
   

   	£1		10p	1p
   £	1	.	3	5
   + £	1	.	2	0
   £	2	.	5	5

3. Take the total cost away from the money paid. What is left is the change.
   £5.00 − £2.55 = £2.45
   

   	£1		10p	1p
   £	45	.	90	100
   − £	2	.	5	5
   £	2	.	4	5

4. Write the answer.
   The change is £2.45

Check. Add the change to the total: £2.55 + £2.45 = £5.00. ✓

Watch out. Multiply first, then add, then subtract from the money paid.

Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.

Method. First find the total length cut off. Then take it away from the whole ribbon.

1. Step 1: add the two pieces. This gives the total length cut off.
   1.25 m + 0.75 m
   

   	O		t	h
   	1	.	2	5
   +	0	.	7	5
   	2	.	0	0
   	1		1

   1.25 + 0.75 = 2.00 m
2. Step 2: take the total away from the whole ribbon. Write 3.5 as 3.50 so the decimal points and digits line up.
   3.50 m − 2.00 m
   

   	O		t	h
   	3	.	5	0
   −	2	.	0	0
   	1	.	5	0

   3.50 − 2.00 = 1.50 m
3. Write the answer. 1.50 m is the same as 1.5 m.
   1.5 m

Check. Add back: 1.5 + 1.25 + 0.75 = 3.5. ✓

Watch out. Take away the TOTAL of the two pieces, not just one piece.