Understanding Scientific Notation for the FTCE General Knowledge Math Test

What is the scientific notation for the number 0.000000975?

• A. 9.75 x 10⁻⁷
• B. 9.75 x 10⁶
• C. 97.5 x 10⁻⁹
• D. 0.975 x 10⁻⁶

Answer: (A)

The correct scientific notation for the number 0.000000975 is expressed as 9.75 x 10⁻⁷. In scientific notation, a number is represented as a product of a coefficient and a power of ten. The coefficient must be a number greater than or equal to 1 and less than 10. In this case, to convert 0.000000975 into scientific notation, you first shift the decimal point to the right until you have a number between 1 and 10. Moving the decimal point 7 places to the right gives you 9.75. Since you moved the decimal to the right, the exponent for the power of ten is negative, indicating a value less than one. Thus, you get 9.75 x 10 to the power of negative seven. The other options do not properly represent the number in scientific notation. The second choice involves an exponent that does not accurately reflect the original value, while the third choice incorrectly shifts the decimal to yield a coefficient greater than 10. The last choice also misplaces the decimal and the exponent in a way that does not correspond to the initial numerical value.

Have you ever found yourself staring at a tiny number, wondering how to make sense of it? For students prepping for the FTCE General Knowledge Math Test, mastering scientific notation is vital. So, let’s break it down in a way that makes it stick, shall we?

To illustrate, consider the number 0.000000975. Your task is to express this seemingly complex figure in scientific notation. What’s the right way to do that? Here’s the scoop: the scientific notation for 0.000000975 is 9.75 x 10⁻⁷. Yep, you read that right! But why does this conversion work? Let’s dive in.

A Quick Refresher on Scientific Notation

Scientific notation allows us to represent very large or very small numbers in a more manageable way. Think of it like giving numbers a new outfit—something snazzy that’s easier to analyze. In this format, we express a number as the product of a coefficient (which must be between 1 and 10) and a power of ten. Confusing? Let me explain it simply.

When you take the decimal point in our original number (0.000000975) and shift it to the right until you land on a number between 1 and 10, you’ll find 9.75. That’s your coefficient! The catch? For every place you shift the decimal to the right, you have to subtract from the exponent of ten. Since we shifted it 7 times, we use a negative exponent: 10⁻⁷. So, voilà—9.75 x 10⁻⁷ is the golden ticket!

Why Other Options Don’t Work

You might wonder about other possible answers. Let’s break them down just for clarity.

• Option A: 9.75 x 10⁻⁷. Correct! This matches our derived notation.

• Option B: 9.75 x 10⁶. Nope! The exponent is too positive, making it way too large.

• Option C: 97.5 x 10⁻⁹. This one’s misleading; the coefficient exceeds 10, which violates our rules!

• Option D: 0.975 x 10⁻⁶. Here, the coefficient doesn’t fall within the required range either.

Putting It Into Context

As daunting as it might seem, practicing with numbers like these can bolster your confidence. You can think of scientific notation like GPS for math—it helps you navigate tricky values with ease. And remember, the more you practice, the more you’ll start recognizing patterns and rules. Try turning some of your own numbers into scientific notation!

Let’s explore a quick analogy. Imagine you’re packing for a vacation. You wouldn’t stuff your suitcase full of random items, right? You’d neatly fold everything, maybe even compress it, to save space. Scientific notation is similar—it makes unwieldy numbers neat and tidy, allowing you to work with them effortlessly in the realm of mathematics.

Wrapping It Up

So next time you’re faced with a number like 0.000000975, don’t let it throw you off. Remember the steps: shift that decimal, determine your coefficient, apply the proper power of ten, and you’re golden. And yes, practice can indeed make perfect (or at least better!), so keep tackling those challenges and watch your math confidence soar. Don’t forget, every small victory counts in your preparation for the FTCE General Knowledge Math Test!