Year 6 Arithmetic (SATs) Decimals and percentages: check-up and practice test questions

Method. Count the decimal places.

1. Count the places. 0.37 has two decimal places.
   two
2. Write over 100. 0.37 = 37/100.
   37/100
3. Write the answer.
   37/100

Check. 37 ÷ 100 = 0.37. ✓

Method. Find the hundredths column.

1. Find the column. The 4 is the second digit after the point, so it is in the hundredths column.
   hundredths
2. Write the value. 4 hundredths is 0.04.
   0.04
3. Write the answer.
   0.04

Check. 6 + 0.2 + 0.04 + 0.008 = 6.248. ✓

Method. Multiply by 100 moves the digits two places left.

1. Move each digit two places left. The point moves to the right of the 5.
   2.75 → 275
2. Write the answer.
   275

Check. 275 ÷ 100 = 2.75. ✓

Method. Test each choice against the question.

1. Read what the question asks. Decide what you need to find or check.
2. Test the choice. 0.680 has 6 tenths, the same as 0.608, but 8 hundredths is more than 0 hundredths.
   0.68 is right
3. Reject the other choices. 0.608 has 0 hundredths and 0.68 has 8, so 0.608 is smaller.
   0.608 are not right
4. Write the answer.
   0.68

Check. 0.68 is right. ✓

Method. Look at the third decimal digit.

1. Find the place you are rounding to. Rounding to two decimal places means keeping 2 decimal places.
   keep 2 places
2. Look at the next digit. The digit after the place is 4. If it is 5 or more, round up; if less, round down.
   digit 4
3. Write the rounded number. 5.6249 rounds to 5.62.
   5.6249 → 5.62
4. Write the answer.
   5.62

Check. 5.62 is nearer to 5.6249 than 5.63 is. ✓

Method. Multiply 236 by 4, then put the point back.

1. Ignore the decimal point for now. Multiply the digits 236 by 4, as whole numbers.
   236 × 4 = 944
2. Put the decimal point back. 2.36 has 2 decimal places, so the answer has 2.
   944 → 9.44
3. Write the answer.
   9.44

Check. About 2.4 × 4 = 9.6, close to 9.44. ✓

Method. Divide 48 by 6, then place the point.

1. Divide the digits as a whole number. 48 ÷ 6 = 8 remainder 0.
   48 ÷ 6 = 8 r 0
2. Place the decimal point. Put the point in the answer directly above the point in 4.8, and count the places.
   4.8 ÷ 6 = 0.8
3. Write the answer.
   0.8

Check. 0.8 × 6 = 4.8. ✓

Method. Find 1%, then multiply by 25.

1. Find 1%. 1% is one hundredth, so divide the amount by 100.
   360 ÷ 100 = 3.6
2. Multiply by 25. 25% is 25 lots of 1%.
   3.6 × 25 = 90
3. Write the answer.
   90

Check. A quarter of 360 is 90. ✓

Method. Make the bottom 1000, then multiply by 100 for the percentage.

1. Decimal. 3/8 = 375/1000 = 0.375.
   0.375
2. Percentage. 0.375 × 100 = 37.5, so 37.5%.
   37.5%
3. Write the answer.
   0.375, 37.5%

Check. 0.375 × 8 = 3. ✓

Method. Add zeros at the end of the decimal and compare.

1. Compare the numbers. 2.50 is 2 and 50 hundredths, which is the same as 2.5.
   2.50 = 2.5
2. Multiply. 2.5 × 4 = 10 in both cases.
   10
3. Write the answer.
   Because 2.50 = 2.5, so both multiply to 10.

Check. The zero at the end does not change the value. ✓

Method. Write over 10, then simplify.

1. Write over 10. 0.8 = 8/10.
   8/10
2. Simplify. Divide by 2 to get 4/5.
   4/5
3. Write the answer.
   4/5

Check. 4/5 = 0.8. ✓

Method. Find the hundredths column.

1. Find the column. Count the places after the point: 0 tenths, then 5 hundredths.
   hundredths
2. Write the value. 5 hundredths is 0.05.
   0.05
3. Write the answer.
   0.05

Check. 3 + 0 + 0.05 + 0.004 = 3.054. ✓

Method. Use two partial products, then put the point back.

1. Multiply by the ones digit. Multiply the digits 625 by 2.
   625 × 2 = 1250
2. Multiply by the tens digit. Multiply the digits 625 by 10, which is 1 tens.
   625 × 10 = 6250
3. Add the two parts. Add the partial products.
   1250 + 6250 = 7500
4. Put the decimal point back. 6.25 has 2 decimal places, so the answer has 2.
   7500 → 75.00
5. Write the answer.
   75.00

Check. About 6 × 12 = 72, close to 75.00. ✓

Method. Divide 96 by 12, then place the point.

1. Divide the digits as a whole number. 96 ÷ 12 = 8 remainder 0.
   96 ÷ 12 = 8 r 0
2. Place the decimal point. Put the point in the answer directly above the point in 9.6, and count the places.
   9.6 ÷ 12 = 0.8
3. Write the answer.
   0.8

Check. 0.8 × 12 = 9.6. ✓

Method. Look at the third decimal digit.

1. Find the place you are rounding to. Rounding to two decimal places means keeping 2 decimal places.
   keep 2 places
2. Look at the next digit. The digit after the place is 5. If it is 5 or more, round up; if less, round down.
   digit 5
3. Write the rounded number. 7.8359 rounds to 7.84.
   7.8359 → 7.84
4. Write the answer.
   7.84

Check. 7.84 is nearer than 7.83. ✓

Method. Find 1%, then multiply by 12.

1. Find 1%. 1% is one hundredth, so divide the amount by 100.
   250 ÷ 100 = 2.5
2. Multiply by 12. 12% is 12 lots of 1%.
   2.5 × 12 = 30
3. Write the answer.
   30

Check. 10% is 25 and 2% is 5, so 12% is 30. ✓

Method. Work out both amounts.

1. 35% of 200. 1% of 200 is 2, so 35% is 70.
   70
2. 3/4 of 120. 120 ÷ 4 = 30, and 30 × 3 = 90.
   90
3. Compare. 90 is greater than 70.
   3/4 of 120
4. Write the answer.
   3/4 of 120

Check. 90 > 70. ✓

Method. Find the amount left after the amount sold.

1. Work out the amount sold. 0.6 × 120 = 72, since 0.6 of 120 is 60% of 120.
   72
2. Subtract. 120 - 72 = 48.
   48
3. Write the answer.
   48

Check. 72 + 48 = 120. ✓

Method. Multiply by 100.

1. Multiply by 100. 0.45 × 100 = 45.
   45
2. Write the percentage. 45 out of 100 is 45%.
   45%
3. Write the answer.
   45%

Check. 45/100 = 0.45. ✓

Method. Make the total 100, or divide and multiply by 100.

1. Divide. 26 ÷ 40 = 0.65.
   0.65
2. Multiply by 100. 0.65 × 100 = 65, so 65%.
   65%
3. Write the answer.
   Divide 26 by 40 to get 0.65, then multiply by 100 to get 65%.

Check. 65% of 40 is 26. ✓