Last reviewed: 11 November 2026
Updated November 2026. These Grade 7 decimals notes show how to read the place value and total value of digits in a decimal, and how to multiply or divide a decimal by a whole number and by another decimal. Decimals are a way of writing parts of a whole using tenths, hundredths and thousandths. In 32.456, the digit 4 stands in the tenths place, so its total value is 0.4.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 7 Mathematics numbers sub-strand on decimals in the KICD Grade Seven curriculum designs. Recurring decimals and standard form are later work, covered in the Grade 8 decimals notes. For Grade 7 topics overall, use the Grade 7 mathematics revision guide and the Grade 7 notes hub.
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Place Value and Total Value in Decimals
To the left of the decimal point the places are ones, tens, hundreds and so on, just as with whole numbers. To the right they are tenths, hundredths, thousandths, and so on. Place value is the name of the place; total value is what the digit is actually worth there. OpenStax Prealgebra’s section on decimals uses the same place-value chart.
| Number | Digit | Place value | Total value |
|---|---|---|---|
| 32.456 | 3 | tens | 30 |
| 32.456 | 2 | ones | 2 |
| 32.456 | 4 | tenths | 0.4 |
| 32.456 | 5 | hundredths | 0.05 |
| 32.456 | 6 | thousandths | 0.006 |
So 32.456 = 30 + 2 + 0.4 + 0.05 + 0.006. Reading the number aloud as “thirty-two and four hundred and fifty-six thousandths” is another way to keep the places in order.
Multiplying and Dividing Decimals
To multiply, ignore the decimal points, multiply as whole numbers, then place the point so that the answer has as many decimal digits as the factors have altogether. To divide, you can turn the divisor into a whole number by multiplying both numbers by 10, 100 or 1 000, then divide. The same placement rule is used in OpenStax Prealgebra’s section on decimals and fractions.
Worked example: multiplication
2.35 × 4. First 235 × 4 = 940. 2.35 has two decimal digits and 4 has none, so the product has two decimal digits: 9.40.
1.2 × 0.3. First 12 × 3 = 36. There is one decimal digit in each factor, so two in the product: 0.36.
Worked example: division
4.8 ÷ 3. Three goes into 4 once, remainder 1; bring down 8 to make 18; 3 goes into 18 six times. The point stays above the point in 4.8, so the answer is 1.6.
0.36 ÷ 0.06. Multiply both numbers by 100 to obtain 36 ÷ 6 = 6. Multiplying the dividend and the divisor by the same power of ten does not change the value of the quotient.
Original Practice Questions With Worked Answers
- In 7.208, what is the place value and the total value of the digit 8? Thousandths; total value 0.008.
- Work out 3.07 × 5. 307 × 5 = 1 535, then two decimal places give 15.35.
- Work out 0.8 × 0.4. 8 × 4 = 32, then two decimal places give 0.32.
- Work out 9.6 ÷ 4. 2.4.
- Work out 1.44 ÷ 0.12. Multiply both by 100: 144 ÷ 12 = 12.
- A shop sells 1.25 kg of sugar at KSh 80 per kilogram. What is the cost? 1.25 × 80 = 100, so KSh 100.
Cover the answers and try each question. Whole-number place value, which this topic extends, is in the Grade 7 whole numbers notes. For timed practice use the Grade 7 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the difference between place value and total value?
Place value names the column the digit sits in, such as tenths. Total value is what that digit is worth, so a 4 in the tenths place has total value 0.4.
How do you multiply decimals?
Multiply as if they were whole numbers, then place the decimal point so that the answer has as many decimal digits as the factors have together. 1.2 × 0.3 = 0.36.
How do you divide by a decimal?
Multiply the dividend and the divisor by the same power of ten until the divisor is a whole number, then divide. 0.36 ÷ 0.06 becomes 36 ÷ 6 = 6.
Are recurring decimals part of Grade 7 decimals?
Grade 7 focuses on place value and on multiplying and dividing decimals by whole numbers and by decimals. Recurring decimals and standard form are taught in Grade 8.
Get the marked answers for the Grade 7 Mathematics paper, KSh 20.
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