Adding and Subtracting Decimals with Many Non-Zero Digits

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Student Summary

Base-ten diagrams work best for representing subtraction of numbers with few non-zero digits, such as 0.16−0.090.16 - 0.09. For numbers with many non-zero digits, such as 0.25103−0.046710.25103 - 0.04671, it would take a long time to draw the base-ten diagram. With vertical calculations, we can find this difference efficiently.

Thinking about base-ten diagrams can help us make sense of this calculation.

A setup for the subtraction calculation 0 point 2 5 1 0 3 subtract 0 point 0 4 6 7 1 results in 0 point 1 0 4 3 2. 
A setup for the subtraction calculation 0 point 2 5 1 0 3 subtract 0 point 0 4 6 7 1 results in 0 point 1 0 4 3 2. The number 0 point 2 5 1 0 3 is on top with the subtract 0 point 0 4 6 7 1 beneath, and the 0 from the first number lines up vertically with the 0 from the second number, the 2 from the first number lines up vertically with the 0 from the second, the 5 from the first number lines up vertically with the 4 from the second, and so on. The 1 in the thousandths place of the first number is unbundled to make ten groups of ten thousandths. The five in the hundredths place has 1 unbundled to make 4 hundredths and 10 thousandths.

The thousandth in 0.25103 is decomposed to make 10 ten-thousandths so that we can subtract 7 ten-thousandths. Similarly, one of the hundredths in 0.25103 is decomposed to make 10 thousandths.

Visual / Anchor Chart

Standards

Addressing
6.NS.3

Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.