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Convert Between Standard and Scientific Notation

Students write numbers in scientific notation (a × 10ⁿ, 1 ≤ a < 10) and convert back to standard form. They practice with both very large numbers (e.g., the distance from Earth to the Sun) and very small numbers (e.g., the size of a cell), connecting the notation to real-world contexts.

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Convert Between Standard and Scientific Notation

Grade 8 · Expressions and Equations: Exponents and Scientific Notation · question 1 of 3

0 of 20

20 rungs. A star at the top.

1.2 × 10^2 =

How it is taught

0:00 of 4:09

Scientific notation is a coefficient times a power of 10, with the coefficient at least 1 and less than 10.

The exponent tells how far the decimal moves.

Read it: Powers of ten as places

0.032 = 3.2 × 10^−2: from 3.2 to 0.032 the digits slide 2 places right, so the power is −2. Each place is one power of ten.

  1. Write both numbers in the columns of places.
  2. Count the places the digits slide, one hop a place.
  3. Left makes a positive power; right makes a negative one.

Each place left is 10 times bigger, and each place right is 10 times smaller.

So 2 places right is 10 × 10 times smaller: 10^−2.

Count places, not zeros: 3600 has 2 zeros, but the digits of 3.6 slide 3 places to make it.

Each place the digits slide is one power of ten: left is positive, right is negative.

Counting the zeros: 3600 has 2 zeros, so writing 3.6 × 10^2.

Count the places the digits slide: from 3.6 to 3600 is 3 places left, so 3.6 × 10^3.

25000 = 2.5 × 10^___ — 4. The digits slide 4 places left from 2.5 to 25000: 10^4.

93,000,000 = 9.3 × 10⁷

The Sun is about ninety-three million miles from Earth. That's a huge number — let's write it more compactly.

Here it is in standard form: a nine, a three, and six zeros.

Every whole number has an invisible decimal point sitting right at the very end.

Earth to the Sun93,000,000 milesCan we write that more compactly?Standard form93,000,000•invisible decimalWe need 1 ≤ a < 10← 7 places•Scientific notation9.3×107↕ same value ✓ANSWER9.3 × 10⁷miles to the Sun
Grade 8 · The Earth-to-Sun distance

Scientific notation needs exactly one non-zero digit in front of the decimal — a number from 1 up to 10.

So we slide that decimal point to the left until it lands right after the nine.

It moved seven places. Hold onto that seven — it becomes our exponent.

The number in front becomes nine point three. We can drop the trailing zeros.

Then we multiply by ten to the seventh power. The seven counts how many places we moved.

If we slid the decimal back seven places to the right, we'd land on ninety-three million again. Same value.

So 93,000,000 equals 9.3 times 10 to the seventh. Scientific notation tames huge numbers!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
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Divide within 100

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MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

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