Primary 4 Decimals
A decimal uses a decimal point to separate whole numbers from parts of a whole. Digits to the right of the point show tenths, hundredths and thousandths.
Keywords
- Decimal point
- The mark separating whole-number and fractional places.
- Tenths
- The first place to the right of the decimal point.
- Hundredths
- The second place to the right of the decimal point.
- Thousandths
- The third place to the right of the decimal point.
- Equivalent decimal
- A decimal with the same value, such as 0.5 and 0.50.
- Decimal place (dp)
- A digit position to the right of the decimal point.
Place and place value
To the right of the decimal point, each place is one tenth of the place before it. In 36.478, the 4 is worth 0.4, the 7 is worth 0.07 and the 8 is worth 0.008.
Explore 36.478
Tap a digit to see its place and value in the same chart.
| Place | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| Digit | . | |||||
| Place value | 30 | 6 | · | 0.4 | 0.07 | 0.008 |
Tap a digit to connect its place with its value.
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What is the place and value of each digit in 36.478?
- 3 is in the tens place, so it is worth 30. 6 is in the ones place, so it is worth 6.
- 4 is in the tenths place, so it is worth 0.4.
- 7 is in the hundredths place, so it is worth 0.07.
- 8 is in the thousandths place, so it is worth 0.008.
Answer: 36.478 = 30 + 6 + 0.4 + 0.07 + 0.008.
Try together
What are the place and value of the 5, 8 and 3 in 4.583?
Reveal the answer
5 is in the tenths place and is worth 0.5. 8 is in the hundredths place and is worth 0.08. 3 is in the thousandths place and is worth 0.003.
Compare and order decimals using a chart
Line up the decimal points, write a placeholder zero if needed, and compare from the largest place. The first different place decides the order.
Order 0.45, 0.5, 0.65 and 1.2
| Number | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| 0.45 | 0 | . | 4 | 5 |
| 0.5 | 0 | . | 5 | |
| 0.65 | 0 | . | 6 | 5 |
| 1.2 | 1 | . | 2 |
Show the first step.
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Arrange 0.45, 0.5, 0.65 and 1.2 in increasing order.
- Line up the decimal points. Write 0.5 as 0.50 and 1.2 as 1.20 so all numbers show hundredths.
- Compare ones first: 1.20 has 1 one, while the others have 0 ones. It is the largest.
- For the three numbers with 0 ones, compare tenths: 4, 5 and 6. This orders them without comparing hundredths.
- From smallest to largest: 0.45, 0.50, 0.65, 1.20.
Answer: 0.45 < 0.5 < 0.65 < 1.2.
Try together
Put 1.08, 1.8 and 1.18 in increasing order.
Reveal the answer
1.08 < 1.18 < 1.80 (the same as 1.8).
Express fractions as decimals
When the denominator is a factor of 10 or 100, rename the fraction in tenths or hundredths. The denominator then tells you how many decimal places to write.
Change 34 to a decimal
Show the first step.
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Express 34 as a decimal.
- 4 × 25 = 100, so multiply the numerator and denominator by 25.
- 3 × 25 = 75, giving 75 hundredths.
- 75 hundredths is written 0.75.
Answer: 34 = 75100 = 0.75.
Try together
Express 720 as a decimal.
Reveal the answer
20 × 5 = 100, so 720 = 35100 = 0.35.
Round decimals to 1 or 2 decimal places
Point to the place being rounded, then circle the digit immediately to its right. A deciding digit of 5 or more rounds up; 4 or less rounds down.
Round 4.786
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Round 4.786 to 1 decimal place and 2 decimal places.
- For 1 decimal place, point to the tenths digit 7 and circle the hundredths digit 8. Round up: 4.786 ≈ 4.8.
- For 2 decimal places, point to the hundredths digit 8 and circle the thousandths digit 6. Round up: 4.786 ≈ 4.79.
Answer: 4.786 ≈ 4.8 (1 dp) and 4.786 ≈ 4.79 (2 dp).
Try together
Round 6.342 to 1 dp and 2 dp.
Reveal the answer
6.342 ≈ 6.3 (1 dp) and 6.342 ≈ 6.34 (2 dp).
Add and subtract decimals
Place digits in their correct columns and line up the decimal points. Use a zero to show a missing decimal place when needed, then work from right to left.
Work with 12.75 and 3.20
| Tens | Ones | . | Tenths | Hundredths | |
|---|---|---|---|---|---|
| First | 1 | 2 | . | 7 | 5 |
| + | 3 | . | 2 | 0 | |
| Answer | . |
Show the first step.
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Work out 12.75 + 3.20 and 12.75 − 3.20.
- Place 1 and 2 in tens and ones; place 7 and 5 in tenths and hundredths. Put the decimal point in its own column.
- Write 3 in ones, 2 in tenths and 0 in hundredths. Line up the points before calculating.
- Add to get 15.95 or subtract to get 9.55. Keep the point aligned in the answer.
Answer: 12.75 + 3.20 = 15.95; 12.75 − 3.20 = 9.55.
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Work out 5.46 + 2.30 and 5.46 − 2.30.
Reveal the answer
5.46 + 2.30 = 7.76; 5.46 − 2.30 = 3.16.
Multiply and divide decimals by a 1-digit whole number
Work place by place, just as with whole numbers. Keep the decimal point aligned so ones, tenths and hundredths stay in their correct places.
Work with decimals
2.34 × 3 = ?
| Ones | . | Tenths | Hundredths | |
|---|---|---|---|---|
| Regroup | ||||
| Number | 2 | . | 3 | 4 |
| × | 3 | |||
| Answer | . |
7.56 ÷ 3 = ?
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Work out 2.34 × 3 and 7.56 ÷ 3.
- For multiplication, 4 hundredths × 3 = 12 hundredths. Write 2 hundredths and regroup 1 tenth.
- 3 tenths × 3, plus 1 regrouped tenth, makes 10 tenths. Write 0 tenths and regroup 1 one. Then 2 ones × 3 + 1 one = 7 ones. So 2.34 × 3 = 7.02.
- For division, 7 ones ÷ 3 = 2 ones with 1 one left. Bring down 5 tenths to make 15 tenths; 15 ÷ 3 = 5 tenths.
- Bring down 6 hundredths; 6 ÷ 3 = 2 hundredths. Place the point directly above the point in 7.56, giving 2.52.
Answer: 2.34 × 3 = 7.02; 7.56 ÷ 3 = 2.52.
Try together
Work out 1.24 × 2 and 8.64 ÷ 2.
Reveal the answer
1.24 × 2 = 2.48; 8.64 ÷ 2 = 4.32.
Divide whole numbers to get a decimal quotient
When whole-number division leaves a remainder, place a decimal point in the quotient and add a zero after the dividend’s decimal point. Continue dividing in tenths.
Divide 7 by 2
7 ÷ 2 = ?
Show the first step.
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Work out 7 ÷ 2. Give the quotient as a decimal.
- 2 goes into 7 three times. Write 3 above the 7; subtract 6 to leave 1.
- Write 7 as 7.0. Put the decimal point in the quotient directly above the dividend’s point.
- Bring down the 0 tenths. The remaining 1 whole is 10 tenths.
- 10 tenths ÷ 2 = 5 tenths. Write 5 after the decimal point, so 7 ÷ 2 = 3.5.
Answer: 7 ÷ 2 = 3.5.
Try together
Work out 9 ÷ 2. Give the quotient as a decimal.
Reveal the answer
9 ÷ 2 = 4.5.