Scientific Notation Add/Subtract Lab

Use these worksheets to practice matching powers of 10 before adding or subtracting numbers in scientific notation.

Review how to add, subtract, multiply, and divide numbers written in scientific notation.

Choose addition or subtraction, then rewrite the term with the smaller exponent so both powers of 10 match.

Combine the matching coefficients and keep the common power of 10.

Use the green and red feedback to identify which steps are correct and which steps still need revision.

Scientific notation terms cannot be added or subtracted directly until their powers of 10 are the same.

Rewriting one term changes its coefficient and exponent but does not change its value.

Once the powers match, keep the common power of 10 and combine only the coefficients.

Scientific notation: A way to write a number as a coefficient multiplied by a power of 10.

Coefficient: The number in front of the power of 10, such as \(4.6\) in \(4.6 \times 10^7\).

Power of 10: An expression such as \(10^2\), \(10^5\), or \(10^{-3}\).

Like terms: Terms that can be combined because they have the same variable part or the same power of 10.

Equivalent expression: A rewritten expression with the same value, such as \(3.2 \times 10^4 = 0.32 \times 10^5\).

Before adding or subtracting, rewrite the expressions so the powers of 10 match.

\(a \times 10^m + b \times 10^n\) can only be combined directly when \(m=n\).

When the powers match, combine the coefficients and keep the common power of 10.

\(a \times 10^n + b \times 10^n = (a+b)\times10^n\)

Subtraction follows the same process: match the powers first, subtract the coefficients, and then write the result in scientific notation.

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