Decimals

1.0 Numbers · 1.4 Decimals

Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.4 Decimals (6 lessons)

Lesson objectives

By the end of this topic, you will be able to:

A decimal uses place value to show parts of a whole. The digits after the point are tenths, hundredths, thousandths, and so on.

a) Place value and total value

Each place after the point is ten times smaller than the one before it.

In 24.573 the 5 is in the tenths place, so its total value is 0.5. The 7 is in the hundredths place, worth 0.07. The 3 is thousandths, worth 0.003.

The place value is what the position is worth. The total value is the digit multiplied by that.

b) Multiplying by a whole number

Multiply as if the point were not there, then put it back.

For 3.2 × 4, work out 32 × 4 = 128. There was one decimal place, so the answer has one: 12.8.

c) Multiplying by a decimal

Count the decimal places in both numbers, add them, and give the answer that many.

In 0.4 × 0.3 there is one place in each, so the answer has two: 0.12.

The answer is smaller than both numbers. Multiplying by something less than 1 always shrinks, which surprises learners used to whole numbers.

d) Dividing by a whole number

Divide as usual, keeping the point in line above.

For 7.5 ÷ 3, the answer is 2.5, with the point directly above where it was.

e) Dividing by a decimal

Multiply both numbers by 10, or 100, until the number you are dividing by is whole.

Doing the same to both keeps the answer unchanged, exactly as with equivalent fractions.

Then divide normally, and check by multiplying back.

f) Where this is used

Money is written in decimals. Measurements of length and mass are decimal. A shopkeeper pricing goods per kilogram divides decimals every day.

Words to know

Decimal point — the point separating the whole-number part of a number from its fractional part.
Tenths, hundredths, thousandths — the place values immediately after the decimal point, each one-tenth the size of the one before.
Divisor — the number you are dividing by.

:::checkpoint Check yourself

Try the exercises below — on decimal place value, multiplication and division.