1/15
00:00

U.5 Compose and decompose decimal numbers

Loading questions...

What does it mean to compose and decompose decimal numbers?

Composing a decimal means putting smaller place value parts together to make a whole or a larger decimal. Decomposing means breaking a decimal into its place value parts to see how each digit contributes to the number’s value.

Examples:
  • Compose: 0.5 + 0.08 + 0.002 = 0.582
  • Decompose: 7.432 = 7 + 0.4 + 0.03 + 0.002
Note

Each place to the right of the decimal point represents a fraction with a denominator of ten, one hundred, one thousand, and so on.

Understanding place value in extended decimals

In decimals, each place has a specific value that is ten times smaller than the place to its left. The pattern continues from tenths to hundredths, thousandths, millionths, and even billionths.

Place Value Example:
  • In 9.74532819:
  • 9 → ones place (9 × 1)
  • 7 → tenths (7 × 1/10 = 0.7)
  • 4 → hundredths (4 × 1/100 = 0.04)
  • 5 → thousandths (5 × 1/1,000 = 0.005)
  • 3 → ten-thousandths (3 × 1/10,000 = 0.0003)
  • 2 → hundred-thousandths (2 × 1/100,000 = 0.00002)
  • 8 → millionths (8 × 1/1,000,000 = 0.000008)
  • 1 → billionths (1 × 1/1,000,000,000 = 0.000000001)
Note

The place value chart for decimals never ends—it continues dividing by ten for each new place to the right.

How to compose decimal numbers

To compose a decimal, add together the values of each place. This shows how individual parts combine to make one complete number.

Steps:
  • Write each part using place value: 5 + 0.2 + 0.04 + 0.006 + 0.00008 + 0.000009
  • Add the values together: 5.246089
  • The composed number is 5.246089
Note

When adding or writing decimals, always align the decimal points so that digits in the same place value line up vertically.

How to decompose decimal numbers

To decompose a decimal, break it apart into its individual place value parts. Each digit represents a fraction of ten based on its position.

Examples:
  • 8.9046 = 8 + 0.9 + 0.004 + 0.0006
  • 0.700345 = 0.7 + 0.0003 + 0.00004 + 0.000005
  • 12.030008019 = 10 + 2 + 0.03 + 0.000008 + 0.000000019
Note

Decomposing helps you understand that each decimal digit represents a specific part of one whole. This is useful when comparing, rounding, or estimating decimals.

Visualizing decimals to the billionths place

Models such as grids, number lines, and base-ten blocks help you picture how decimals grow smaller as you move to the right. Each new place is one-tenth of the place before it.

Example:
  • A square divided into 1,000 equal parts can represent thousandths.
  • Shading 237 of those parts represents 0.237.
  • If the square were divided into one billion parts, shading one would represent 0.000000001 (one billionth).
Note

Understanding very small decimals helps build a strong number sense for measurement, data, and scientific notation later on.