WRITING A NUMBER IN STANDARD FORM

To translate between scientific notation and standard notation, move the decimal point the number of places indicated by the exponent in the power of 10.

When the exponent is positive, move the decimal point to the right and add placeholder zeros as needed.

When the exponent is negative, move the decimal point to the left.

Example 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.

Example 2 : 

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.

Reflect

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

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.

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

When 5.3 is written in scientific notation, we have 

5.3  =  5.3 x 10⁰

So, the exponent on 10 is 0.

3. Explain whether 0.9 x 10^-5 is written in scientific   notation. If not, write the number correctly in scientific notation.

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

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

3 x 10^-2 is larger. 

Because its exponent is greater.

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