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Back to Exercise: Perform operations with numbers expressed in scientific notation

Exercises: Computing with Scientific Notation

Grade 8·20 problems·~35 min·Common Core Math - Grade 8·container·8-ee-a-4
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which is proper scientific notation?

2.

Simplify 107÷10310^7 \div 10^3 as a power of 10.

3.

A calculator shows 2.4E6. What does this mean?

B

Fluency Practice

1.

Compute (3×104)(2×105)(3 \times 10^4)(2 \times 10^5) and give your answer in proper scientific notation.

2.

Compute (4×103)(5×106)(4 \times 10^3)(5 \times 10^6) in proper scientific notation.

3.

Compute (3.2×105)+(4.1×105)(3.2 \times 10^5) + (4.1 \times 10^5).

4.

Rewrite 6.0×1046.0 \times 10^4 with power 10510^5 so you can add it to 3.2×1053.2 \times 10^5.

5.

Convert 2.1E-5 to standard scientific notation.

C

Varied Practice

Step flow for subtracting scientific notation by matching exponents first
1.

Compute (5.0×108)−(3.0×107)(5.0 \times 10^8) - (3.0 \times 10^7) in proper scientific notation.

2.

Compute (1.5×108)÷384000(1.5 \times 10^8) \div 384000 (about Earth-Sun distance divided by Earth-Moon distance).

3.

Compute (9.8×106)+(4.5×106)(9.8 \times 10^6) + (4.5 \times 10^6) in proper scientific notation.

4.

A calculator shows -4.7E3. Which value is equivalent?

D

Word Problems

1.

The Mid-Atlantic Ridge spreads at about 2.5 centimeters per year for 10 million years.

How far does it spread in kilometers?

2.

A data center does 4.2×1094.2 \times 10^9 operations each second. One day is 8.64×1048.64 \times 10^4 seconds.

1.

How many operations are done in one day? Give scientific notation.

2.

A second center does 1.5×10141.5 \times 10^{14} operations per day. Which center does more, and by about how much?

3.

A calculator returns 6.02E23 for a chemistry quantity.

Which is the correct interpretation?

E

Error Analysis

Wrong versus right comparison for adding scientific notation with unmatched exponents
1.

Lina computes:
(3×105)+(6×104)(3 \times 10^5) + (6 \times 10^4)

Lina writes:
9×1099 \times 10^9

What error did Lina make?

2.

Noah rewrites 6×1046 \times 10^4 as 6×1056 \times 10^5 to match exponents before adding.

Why is Noah's rewrite invalid?

F

Challenge / Extension

Step ladder for division and normalization from 0.3 times ten to the negative seven into 3 times ten to the negative eight
1.

Compute and normalize: (2.4×10−3)÷(8×104)(2.4 \times 10^{-3}) \div (8 \times 10^4).

2.

A tectonic rate is 2.5×10−52.5 \times 10^{-5} km/year. Explain why this can be a poor communication choice and propose a better unit expression.

0 of 20 answered