Express each of the following as an “ordinary” decimal number. a. 4.83 ×10^2 b. 7.221 ×10^-4 C.

Express each of the following as an “ordinary” decimal...

Key Concepts

Understanding Exponents

Exponents indicate how many times the base (in this context, 10) is multiplied by itself. They provide a structured way to manage and manipulate the scale of numbers, facilitating the conversion between scientific and ordinary decimal notation.

Multiplication by Powers of 10

Multiplication by powers of 10 adjusts the position of the decimal point. When the power is positive, the decimal point moves to the right, increasing the number's magnitude. Conversely, when the power is negative, the decimal point shifts to the left, making the number smaller.

Scientific Notation

Scientific notation is a method of representing numbers as the product of a coefficient (a number typically between 1 and 10) and a power of 10. This method is especially useful for expressing very large or very small numbers in a concise and manageable form.

Ordinary Decimal Notation

Ordinary decimal notation expresses numbers using the base-10 system without exponents. Converting from scientific notation to ordinary decimal involves moving the decimal point according to the exponent value, which represents the number of places to shift.

Transcript

00:01 Today, we'll be rewriting each of the below numbers in ordinary decimal notation.

00:06 Now, the first thing that we should notice is that all of the numbers below are currently in standard scientific notation.

00:12 That means we need to convert from this to ordinary decimal notation.

00:17 Let's start with a.

00:18 A is 4 .83 times 10 to the positive, sorry, too.

00:23 Since the exponent is positive, that means we're moving the decimal place up to the right.

00:30 So, from between the 4 and 8, we go once, twice.

00:36 And so what that would look like is 483, and the decimal point is there with an imaginary 0 after.

00:43 That's our answer for a.

00:46 Moving on to b.

00:47 Here, the exponent on the 10 is a negative 4.

00:50 Because the number is negative, we are moving the decimal point backwards to the left.

00:55 So, that would mean that we move the decimal point backwards once.

01:01 And then we move it back three more times.

01:03 But then since there are no more numbers there, that means we're going to have three zeros in front of the 7 -221.

01:09 Our answer is going to end up being 0 .0 .000 -7 -221.

01:20 Moving out to c, interestingly, our exponent is 0.

01:25 Now 10 to the 0 is equal to 1, which means that this number is equal to 6 .1 times the 1.

01:32 1, which is simply 6 .1.

01:36 So that's our answer for c.

01:40 Now let's move on to d.

01:42 Similarly, like part b in d, our exponent is a negative 8.

01:47 So that means we are moving the decimal point back to the left.

01:52 So we move the decimal point back once.

01:54 And now because we have no more numbers to push back, we're going to add 7 zeros in order to move the decimal point back a total of eight places.

02:03 That means we end up with the number zero point.

02:06 Now we add seven zeros.

02:08 One, two, three, four, five, six, seven, and then nine, one, one.

02:17 That is our final answer for d.

02:20 Let's move on to e.

02:22 Here, our exponent on the 10 is a positive six.

02:26 That means we are moving the decimal point to the right forwards.

02:30 So we're going to move the decimal point one, two, three times and now we need to move it through more times so we're going to add three zeros at the end of this number which means we have four two two one and three zeros so that's our final answer for e moving on to f here our exponent is a negative three which means we're moving the decimal point to the left so we'll move the decimal point once then add because we moved it once and we want to move it a total three times two more zeros in front of the one two two two so we'll have zero point one two zeros one two two that's our final answer for f now let's move on to g in g our exponent is a positive three so we are going to move our decimal point to the right three times so it'll go once twice, three times.

03:33 And so basically our answer here is 9 ,99 with an imaginary decimal and zero at the end.

03:44 So that's our answer for g.

03:46 Moving on to h, our exponent is negative...

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