WRITING NUMBERS IN STANDARD NOTATION WORKSHEET

Question 1 : 

Write 3.5 x 10⁶ in standard notation. 

Question 2 :

Explain why the exponent in 3.5 x 10⁶ is 6, while there are only 5 zeros in 3,500,000.

Question 3 : 

Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10^-6  meter. Write 2.33 x 10^-6 in standard notation. 

Question 4 :

What is the exponent on 10 when you write 5.3 in scientific notation ?

Question 5 :

Explain whether 0.9 x 10^-6 is written in scientific notation. If not, write the number correctly in scientific notation.

Question 6 : 

Which number is larger, 2 x 10^-3 or  3 x 10^-2 ? Explain.

Detailed Answer Key

Question 1 : 

Write 3.5 x 10⁶ in standard notation. 

Solution : 

Step 1 :

Use the exponent of the power of 10 to see how many places to move the decimal point.

6 places

Step 2 :

Since the exponent of 10 in 3.5 x 10⁶ is positive, we have to write a number less than 3.5.

Since you are going to write a number greater than 3.5, move the decimal point to the right. Add placeholder zeros if necessary.

So, the number 3.5 x 10⁶ in standard notation is  3,500,000.

Question 2 :

Explain why the exponent in 3.5 x 10⁶ is 6, while there are only 5 zeros in 3,500,000.

Answer : 

The decimal point moves 6 places to the right, but one of those places is the 5 tenths in 3.5, so only 5 placeholder zeros are needed.

Question 3 : 

Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10^-6  meter. Write 2.33 x 10^-6 in standard notation. 

Solution : 

Step 1 :

Use the exponent of the power of 10 to see 6 places how many places to move the decimal point.

6 places

Step 2 :

Since the exponent of 10 in 2.33 x 10^-6 is negative, we have to write a number less than 2.33.

Since you are going to write a number less than 2.33, move the decimal point to the left. Add placeholder zeros if necessary.

So, the number 2.33 x 10^-6 in standard notation is 0.00000233.

Question 4 :

What is the exponent on 10 when you write 5.3 in scientific notation ?

Answer :

When 5.3 is written in scientific notation, we have 

5.3  =  5.3 x 10⁰

So, the exponent on 10 is 0.

Question 5 :

Explain whether 0.9 x 10^-6 is written in scientific notation. If not, write the number correctly in scientific notation.

Answer :

No

Because the first factor is less than 1. The decimal point should move to the right and the exponent should decrease by 1 : 9 x 10^-6

Question 6 : 

Which number is larger, 2 x 10^-3 or  3 x 10^-2 ? Explain.

Answer :

3 x 10^-2 is larger

Because its exponent is greater.

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