Add and Subtract Numbers in Scientific Notation

Students add and subtract numbers in scientific notation by first rewriting them with the same power of 10, combining coefficients, then expressing the result in proper scientific notation. They connect this skill to comparing and combining real-world quantities of very different magnitudes.

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

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20 rungs. A star at the top.

A museum's website had 4.6 × 10^3 visits in June and 7.8 × 10^3 visits in July. How many visits did it have in the two months, in standard form?

How it is taught

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To add numbers in scientific notation, first match the powers of 10.

Then add the coefficients and keep that power.

Read it: Scientific notation: operations

5 × 10^7 + 3 × 10^7 counts 10^7s: 5 of them and 3 more make 8 of them, so the sum is 8 × 10^7. The power stays 10^7.

To add or take away, match the powers, then work the numbers.
To multiply, multiply the numbers and add the exponents.
To divide, divide the numbers and take away the exponents.

5 × 10^7 is 5 of the 10^7s, the way 5x is 5 of the x's.

Adding counts them, so the power does not change: 8 × 10^7.

Multiplying multiplies the powers too: 10^7 × 10^7 = 10^14.

Add like powers by their numbers; multiply in two parts, the numbers and the powers.

Adding the exponents: 5 × 10^7 + 3 × 10^7 = 8 × 10^14.

Adding counts the 10^7s: 5 + 3 = 8 of them: 8 × 10^7.

(2 × 10^8) + (4 × 10^8) = ___ × 10^8 — 6. Both are counts of 10^8, like terms: 2 + 4 = 6 of them, and the power stays 10^8.

(3.2 × 10⁴) + (5 × 10³)

Let's add two numbers written in scientific notation. Their powers of ten are different — that's the tricky part.

Here's our problem: three point two times ten to the fourth, plus five times ten to the third.

Look at the exponents: four and three. To add, we need them to match.

Let's rewrite the smaller one. Five times ten cubed — how do we make it ten to the fourth?

Move the decimal one place left: five becomes zero point five, and we bump the exponent up to four.

Now both terms share the same power of ten. We're ready to add.

Add the coefficients: three point two plus zero point five.

That's three point seven.

Keep the shared power of ten. Our answer is three point seven times ten to the fourth.

The coefficient is between one and ten, so it's already in proper scientific notation.

Grade 8 · Combine numbers with different powers of 10

Great work! Match the exponents, add the coefficients, keep the power. That's how we add in scientific notation.

What you see

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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
Climbing now: Divide within 100

An example student.

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.

An example week.

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