Grade 8 · Math

8th grade Scientific notation: write, convert and say how many times larger worksheet

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Scientific notation: write, convert and say how many times larger

Grade 8 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

Tala reads that a heart beats about 3 × 10^9 times in a long life and 6 × 10^4 times in half a day. How many times as many beats is a life?
In Ari's notes, a hair is 4 × 10^-5 m wide and a virus is 8 × 10^-8 m across. How many times as wide is the hair?
Jun reads that the Pacific holds 710,000,000 km³ of water and a big lake 4,900 km³. Rounding each to one digit, about how many times as much?
Kira reads that a year has 31,500,000 seconds and a lesson 2,700. Rounding each to one digit, about how many times as long is a year?
Luz's calculator shows 47 × 10^6. Write it in scientific notation, then round it to one digit. What do you get?
Milo's calculator shows 0.38 × 10^-4. Write it in scientific notation, then round it to one digit. What do you get?
In Pia's science notes, a grown-up body has about 37,000,000,000,000 cells. What is that, rounded to one digit times a power of 10?
Bo reads that light travels about 9,460,000,000,000 km in a year. What is that, rounded to one digit times a power of 10?
In Jun's notes, a speck of dust is 2 × 10^-5 m across and a virus 8 × 10^-8 m. How many times as wide is the speck?
Kira reads that Earth is about 12,742,000 m across. What is that, rounded to one digit times a power of 10?

Scientific notation: write, convert and say how many times larger. Every version has 10 questions, and the answer key prints on the second page.

I can round a big or small amount to one digit times a power of 10.
I can say how many times larger one amount is than another by dividing first parts and subtracting exponents.
I can fix a first part that is below 1 or 10 or more, moving the power the other way.

Standard: 8.EE.A.3

scientific notation: One digit (1–9.9…) times a power of ten: 4 × 10⁶.

round to one digit: Keep the first digit, rounded, then count the places: 3,900,000 ≈ 4,000,000.

how many times larger: Divide the bigger amount by the smaller.

first part: The number before × 10 in scientific notation.

Your child used the number of digits as the power of ten. 3,900,000 has 7 digits but is 3.9 × 10^6: count the places after the first digit.

Your child cut off the digits instead of rounding. 3,900,000 is closer to 4,000,000 than to 3,000,000, so it is about 4 × 10^6.

Your child counted only the zeros after the point. In 0.00008 the point moves 5 places to get past the 8, so it is 8 × 10^-5.

What is the most common mistake with scientific notation: write, convert and say how many times larger?

Your child used the number of digits as the power of ten. 3,900,000 has 7 digits but is 3.9 × 10^6: count the places after the first digit.

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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