Decimal Fractions (Decimals)

ICSE Class 7 · Mathematics · Chapter 4

What this chapter covers

A decimal fraction has 10, 100, 1000 or another power of 10 as its denominator, shown by digits after a decimal point.
Each place after the point is one-tenth of the place on its left: tenths, hundredths, thousandths.
Zeros at the right end of a decimal do not change its value; they help make like decimals.
To change a decimal into a fraction, put the digits over 1 followed by as many zeros as there are decimal places, then simplify.
To change a fraction into a decimal, make the denominator a power of 10 or divide the numerator by the denominator.
A fraction gives either a terminating decimal or a recurring decimal, which is written with a bar.
Multiplying by 10, 100 or 1000 moves the point 1, 2 or 3 places right; dividing moves it left.
When multiplying decimals, the product has as many decimal places as the two numbers together.
When dividing by a decimal, first move the point in both numbers so that the divisor becomes a whole number.
Estimate first and check by the reverse operation to catch a misplaced decimal point.

Write 46.093 in expanded form and name the place of the digit 9.

40 + 6 + (0)/(10) + (9)/(100) + (3)/(1000); the 9 is in the hundredths place.

Which is greater, 0.7 or 0.65? Give a reason.

0.7, because 0.7 = 0.70 and 70 hundredths is more than 65 hundredths.

Write 1.84 as a mixed number in lowest terms.

1.84 = 1 + (84)/(100) = 1(21)/(25).

Convert (11)/(16) into a decimal.

11 ÷ 16 = 0.6875.

Write (4)/(9) as a decimal using bar notation.

(4)/(9) = 0.444ldots = 0.overline4.

Find 0.27 × 1000 and 0.27 ÷ 1000.

270 and 0.00027.

Find 0.15 × 0.3.

15 × 3 = 45 with three decimal places, so 0.045.

Find 6.75 ÷ 0.025.

Multiply both by 1000: 6750 ÷ 25 = 270.