Converting decimals to fractions 1 (ex 1)

Converting decimals to fractions 1 (ex 1)

Let's see if we can write 0.15 as a fraction.

So the important thing here is to look at

what place these digits are in.

So this 1 right over here, this is in the tenths place.

So you could view that as 1 × 1/10.

This 5 right over here is in the hundredths place.

So you could view that as 5 × 1/100.

So if I were to rewrite this,

I can rewrite this as the sum of –

this 1 represents 1 × 1/10,

So that would literally be 1/10 – plus –

And this 5 represents 5 × 1/100.

So it would be plus 5/100.

And if we want to add them up,

if we want to find a common denominator –

(The common denominator is 100.)

Both 10 and –

[100] is the least common multiple.

[100] is a multiple of both 10 and 100.

So we can rewrite this as something over 100 plus something over 100.

This isn't going to change. This was already 5/100.

If we multiply the denominator here by 10 –

(That's what we did. We multiplied it by 10.)

– then we're going to have to multiply this numerator by 10.

And so this is the same thing as 10/100.

And now we're ready to add.

This is the same thing as 10 + 5, is 15/100.

And you could have done that

a little bit quicker just by inspecting this.

You would say, "Look!

My smallest place right over here is in the hundredths place."

Instead of calling this 1/10, I could call this literally 10/100.

Or, I could say this whole thing is 15 100ths.

And now if I want to reduce this to lowest terms,

we can – Let's see,

Both the numerator and the denominator are divisible by 5.

So let's divide them both by 5.

And so the numerator, 15, divided by 5 is 3.

The denominator, 100, divided by 5 is 20.

And that's about as simplified as we can get.