The Lesson
Engineering notation is a way of writing a number. We need to know what number the engineering notation represents. Imagine we wanted to know what number 1.23 × 10^{6} represents.How to Convert Engineering Notation to a Number
Converting engineering notation to a number is easy.Question
What is 1.23 × 10^{6} written in full?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.
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 6.
3
Move the decimal point found in Step 1 by the number of places given by the exponent in Step 2. In engineering notation, it will always be in groups of 3 places. In our example, we will move the decimal places 6 places to the right.
- When we move the decimal point 2 places to the right, we come to the end of the last digit in the number.
- To move the full 6 places, we need to write 0s in the last 4 places.
Answer:
We have taken the number written in engineering notation and written it in full:
1.23 × 10^{6} = 1,230,000
Powers of 10
A power of 10 is 10 raised to a exponent. For example, 10^{3} is a power of 10. The small 3 written beside the 10 means it is raised to an exponent of 3. This means 10 is multiplied by itself 3 times.
10^{3} = 10 × 10 × 10
The answer will have 3 0s after the 1:
10^{3} = 1,000
What Is a Multiple of 3?
The exponent of the power of 10 in engineering notation must be a multiple of 3. A multiple of 3 is a number that results from multiplying 3 by a whole number. Multiples of 3 are:
3, 6, 9, 12, 15, 18, 21...
Multiples of 3 can be negative as well:
−3, −6, −9, −12, −15, −18, −21...