Standard Form - Scientific Notation worksheet - Free Printable

Let's solve the problems step by step.

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1. Write the following in standard form:

We need to express each number in scientific notation, which is of the form:

> $ a \times 10^n $

where:
- $ 1 \leq a < 10 $
- $ n $ is an integer

We move the decimal point so that only one non-zero digit is to the left of the decimal, then count how many places we moved it to determine the exponent of 10.

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#### a) 374 000
Move decimal 5 places left:
$ 3.74 \times 10^5 $

✔ Answer: $ 3.74 \times 10^5 $

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#### b) 1200
Move decimal 3 places left:
$ 1.2 \times 10^3 $

✔ Answer: $ 1.2 \times 10^3 $

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#### c) 745.68
Move decimal 2 places left:
$ 7.4568 \times 10^2 $

✔ Answer: $ 7.4568 \times 10^2 $

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#### d) 29.37
Move decimal 1 place left:
$ 2.937 \times 10^1 $

✔ Answer: $ 2.937 \times 10^1 $

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#### e) 70 000
Move decimal 4 places left:
$ 7 \times 10^4 $

✔ Answer: $ 7 \times 10^4 $

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#### f) 3645.21
Move decimal 3 places left:
$ 3.64521 \times 10^3 $

✔ Answer: $ 3.64521 \times 10^3 $

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#### g) 1210.4
Move decimal 3 places left:
$ 1.2104 \times 10^3 $

✔ Answer: $ 1.2104 \times 10^3 $

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#### h) 74 006
Move decimal 4 places left:
$ 7.4006 \times 10^4 $

✔ Answer: $ 7.4006 \times 10^4 $

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#### i) 1 000
Move decimal 3 places left:
$ 1 \times 10^3 $

✔ Answer: $ 1 \times 10^3 $

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#### j) 98365
Move decimal 4 places left:
$ 9.8365 \times 10^4 $

✔ Answer: $ 9.8365 \times 10^4 $

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✔ Summary for Part 1:

| Problem | Scientific Notation |
|--------|---------------------|
| a) 374 000 | $ 3.74 \times 10^5 $ |
| b) 1200 | $ 1.2 \times 10^3 $ |
| c) 745.68 | $ 7.4568 \times 10^2 $ |
| d) 29.37 | $ 2.937 \times 10^1 $ |
| e) 70 000 | $ 7 \times 10^4 $ |
| f) 3645.21 | $ 3.64521 \times 10^3 $ |
| g) 1210.4 | $ 1.2104 \times 10^3 $ |
| h) 74 006 | $ 7.4006 \times 10^4 $ |
| i) 1 000 | $ 1 \times 10^3 $ |
| j) 98365 | $ 9.8365 \times 10^4 $ |

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2. Expand the following:

Now we convert from scientific notation back to standard form (regular number).

We multiply the coefficient by $ 10^n $, which means moving the decimal point $ n $ places to the right.

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#### a) $ 3.74 \times 10^2 $
Move decimal 2 places right:
$ 3.74 \rightarrow 374 $

✔ Answer: 374

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#### b) $ 8.2 \times 10^2 $
Move decimal 2 places right:
$ 8.2 \rightarrow 820 $

✔ Answer: 820

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#### c) $ 3.153 \times 10^3 $
Move decimal 3 places right:
$ 3.153 \rightarrow 3153 $

✔ Answer: 3153

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#### d) $ 4.789 \times 10^4 $
Move decimal 4 places right:
$ 4.789 \rightarrow 47890 $

✔ Answer: 47890

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#### e) $ 2.5 \times 10^2 $
Move decimal 2 places right:
$ 2.5 \rightarrow 250 $

✔ Answer: 250

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#### f) $ 1.79 \times 10^4 $
Move decimal 4 places right:
$ 1.79 \rightarrow 17900 $

✔ Answer: 17900

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#### g) $ 9.306 \times 10^4 $
Move decimal 4 places right:
$ 9.306 \rightarrow 93060 $

✔ Answer: 93060

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#### h) $ 5.005 \times 10^5 $
Move decimal 5 places right:
$ 5.005 \rightarrow 500500 $

✔ Answer: 500500

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#### i) $ 7 \times 10^2 $
Move decimal 2 places right:
$ 7 \rightarrow 700 $

✔ Answer: 700

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#### j) $ 6 \times 10^4 $
Move decimal 4 places right:
$ 6 \rightarrow 60000 $

✔ Answer: 60000

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✔ Summary for Part 2:

| Problem | Standard Form |
|--------|---------------|
| a) $ 3.74 \times 10^2 $ | 374 |
| b) $ 8.2 \times 10^2 $ | 820 |
| c) $ 3.153 \times 10^3 $ | 3153 |
| d) $ 4.789 \times 10^4 $ | 47890 |
| e) $ 2.5 \times 10^2 $ | 250 |
| f) $ 1.79 \times 10^4 $ | 17900 |
| g) $ 9.306 \times 10^4 $ | 93060 |
| h) $ 5.005 \times 10^5 $ | 500500 |
| i) $ 7 \times 10^2 $ | 700 |
| j) $ 6 \times 10^4 $ | 60000 |

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📌 Final Answers:

#### Part 1: Scientific Notation
a) $ 3.74 \times 10^5 $
b) $ 1.2 \times 10^3 $
c) $ 7.4568 \times 10^2 $
d) $ 2.937 \times 10^1 $
e) $ 7 \times 10^4 $
f) $ 3.64521 \times 10^3 $
g) $ 1.2104 \times 10^3 $
h) $ 7.4006 \times 10^4 $
i) $ 1 \times 10^3 $
j) $ 9.8365 \times 10^4 $

#### Part 2: Expanded Form
a) 374
b) 820
c) 3153
d) 47890
e) 250
f) 17900
g) 93060
h) 500500
i) 700
j) 60000

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