How to Convert Engineering Notation with a Negative Exponent

Converting Engineering Notation with a Negative Exponent

Engineering notation with a negative exponent is a way of writing small numbers. We need to know what number the engineering notation represents.

Imagine we wanted to know what number 1.23 × 10-3 represents.

How to Convert Engineering Notation with a Negative Exponent

Converting engineering notation with a negative exponent to a number is easy.

Question

What is 1.23 × 10−3 written in full?

In engineering notation, a number between 1 and 1,000 (1.23 in this example) is multiplied by a power of 10 that has an exponent that is a multiple of 3 (10−3 in this example).

1.23 times 10 to the minus 3 explained

Step-by-Step:

1

Look at the number between 1 and 1,000. In our example, the number between 1 and 1,000 is 1.23.

Find the decimal point in the number between 1 and 1,000.

1 decimal point 23

Don't forget: If the number does not have a decimal point written, it can be written at the end of the number with a 0 after it (1 = 1.0).

2

Find the exponent of the power of 10. In our example, the exponent of the power of 10 is −3.

exponent of the power of 10 is -3

3

Move the decimal point found in Step 1 by the number of places given by the exponent in Step 2.

In our example, we will move the decimal places 3 places. Because it is minus 3, the decimal point will be moved to the left.

  • When we move the decimal point 1 place to the left, we come past the first digit in the number.

    .1.23
  • To move the full 3 places, we need to write 0s in the next 2 places.

    .001.23

3

Write a 0 before the decimal point.

0.00123

Answer:

We have taken the number written in engineering notation and written it in full:

1.23 × 10−3 = 0.00123

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See Also

What is a power? What is a base? What is an exponent? What is a power of 10? What is a negative exponent? What is a multiple?