How to Write 0.0005 in Scientific Notation: Steps & Tutorial

Instructor: Thomas Higginbotham

Tom has taught math / science at secondary & post-secondary, and a K-12 school administrator. He has a B.S. in Biology and a PhD in Curriculum & Instruction.

Scientists and engineers and others who deal with incredibly big or incredibly small numbers have devised scientific notation to help them work with those big and small numbers. Learn how simple it is in this lesson.

Steps to Solving the Problem

There's small like a mouse, then there's small like a molecule. And representing super small can require super-small numbers: like the size of a hair measured in meters; or the size of a bacterium in inches; or the size of a virus, quark, or gluon in millimeters. We could represent these numbers in basic form, like 0.00000000000000000152. But that can not only get tedious to write, it can also be confusing to look at with precision. To help with such super-small (and super-big) numbers, we can use scientific notation. Sound hard? It's not. Sound fancy? It kind of is. Here, we'll look at how to write 0.0005 in scientific notation.

Scientific notation requires three pretty easy math skills:

  1. Multiplying by Tens
  2. Exponents of Ten
  3. Counting the Number of Decimal Places

You know how multiplying by tens is so easy? Like,

72 x 10 = 720

OR

5.1 x 100 = 510

Scientific notation takes advantage of this. We'll see how later.

Exponents of ten are important, too. If you know what the values of 10 raised to different powers are, you're halfway home. In case you have forgotten, several examples are below.


Ten raised to the Zero Power


Ten to the First Power


Ten to the Second Power


Ten to the Third Power


For multiples of 10 smaller than one:


Ten to the Negative First Power


Ten to the Negative Second Power


Ten to the Negative Fifth Power


What you need to know about exponents of ten is that there are as many zeroes to the right of the decimal point as the exponent is. For example, in 10 to the 2nd power, there are two zeroes after the 1 (or 100).

Taking it just a step further from one of the examples above,

5.1 x 100 = 510


100 equals 10 to the 2nd


therefore,


510 in Scientific notation


The next skill is counting the number of decimal places you need to move to get to a position where you have just one non-zero digit to the left of the decimal point. For example, in 520,000 the decimal is at the end of the number, and between the 5 and 2 is where you need to move. That's five places. For 0.000004901, you need to get to 4.901, which is six places. You're about to see why this is important.

After we've moved the decimal, we take the resulting 'number', which is called the digit term, and put it together in a multiplication statement with the power of 10, which is called the exponential term. Remember, we use negative exponents for small numbers, specifically those that are smaller than 1.

Using the examples above,


520,000 = 5.2 x 10 5


0.000004901 = 4.901 x 10 -6


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