A Peek Beyond the Point

Overview

This chapter introduces decimals as a way of writing numbers between whole numbers. We see how tenths, hundredths and thousandths extend the place value system beyond the decimal point.

Key concepts

• The decimal point separates the whole part from the fractional part.
• Place values after the point: tenths (1/10), hundredths (1/100), thousandths (1/1000).
• Decimals and fractions are two ways of writing the same value.
• Comparing decimals by aligning the decimal points.

Important formulae

• 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000
• Tenths place = first digit after the point
• To compare, add zeros so both decimals have equal digits

Solved example

1. Write 3/4 as a decimal.
2. 3/4 = 75/100.
3. 75/100 = 0.75.

Important questions

1. Write 0.6 and 0.45 as fractions in simplest form.
2. Which is greater, 0.7 or 0.65?
3. Express 2 and 3/10 as a decimal.
4. Write the place value of 5 in 12.358.

Quick revision

Each place after the point is ten times smaller than the one before it. Convert between decimals and fractions, and compare by lining up the decimal points.