**Scientific Notation with Positive Powers of 10 Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on converting numbers from standard form to scientific notation.

Before look at the worksheet, if you would like to like to learn how to convert numbers from standard form to scientific notation,

**Problem 1 :**

Write the given number in scientific notation.

5400000

**Problem 2 :**

Write the given number in scientific notation.

35614.23

**Problem 3 :**

Write the given number in scientific notation.

203005.1

**Problem 4 :**

The weights of various sea creatures are shown in the table. Write the weight of the Blue whale, Gray whale and Whale shark in scientific notation.

Write the weight of each creature in scientific notation.

**Problem 1 :**

Write the given number in scientific notation.

5400000

**Solution :**

Here we don't find decimal point in 5400000. So we have to assume that there is decimal point at the end .

Then, 5400000 ---------> 5400000.

Number of digits between the first non zero digit and the decimal point is 6.

So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)

5400000 = 5.400000 x 10^{6}

5400000 = 5.4 x 10^{6}

Hence, the scientific notation of 5400000 is

5.4 x 10^{6}

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

**Problem 2 :**

Write the given number in scientific notation.

35614.23

**Solution :**

In the given number 35614.23, number of digits between the first non zero digit and the decimal point is 4.

So, the decimal point has to be moved 4 digits to the left and exponent of 10 should be 4 (positive integer)

35614.23 = 3.561423 x 10^{4}

Hence, the scientific notation of 35614.23 is

3.561423 x 10^{4}

**Problem 3 :**

Write the given number in scientific notation.

203005.1

**Solution :**

In the given number 203005.1, number of digits between the first non zero digit and the decimal point is 5.

So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer)

203005.1 = 2.030051 x 10^{5}

Hence, the scientific notation of 203005.1 is

203005.1 = 2.030051 x 10^{5}

**Problem 4 :**

The weights of various sea creatures are shown in the table. Write the weight of the Blue whale, Gray whale and Whale shark in scientific notation.

Write the weight of each creature in scientific notation.

**Solution : **

**Weight of Blue whale in scientific notation : **

In the given weight of Blue whale (250,000 lb), we don't find decimal point. So we have to assume that there is decimal point at the end .

Then,

250,000 -----> 250,000.

Number of digits between the first non zero digit and decimal point is 5.

So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer)

250,000 = 2.50000 x 10^{5}

250,000 = 2.5 x 10^{5}

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Blue whale in scientific notation is

2.5 x 10^{5} lb

**Weight of Gray whale in scientific notation : **

In the given weight of Gray whale (68,000 lb), we don't find decimal point. So we have to assume that there is decimal point at the end .

Then,

68,000 -----> 68,000.

Number of digits between the first non zero digit and decimal point is 4.

So, the decimal point has to be moved 4 digits to the left and exponent of 10 should be 4 (positive integer)

68,000 = 6.8000 x 10^{4}

68,000 = 6.8 x 10^{4}

(Here zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Gray whale in scientific notation is

6.8 x 10^{4} lb

**Weight of Whale shark in scientific notation : **

In the given weight of Whale shark (41,200 lb), we don't find decimal point. So we have to assume that there is decimal point at the end .

Then,

41,200 -----> 41,200.

Number of digits between the first non zero digit and decimal point is 4.

So, the decimal point has to be moved 3 digits to the left and exponent of 10 should be 4 (positive integer)

41,200 = 4.1200 x 10^{4}

41,200 = 4.12 x 10^{4}

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Gray whale in scientific notation is

4.12 x 10^{4} lb

After having gone through the stuff above, we hope that the students would have understood how to convert numbers from standard form to scientific notation.

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