what is 1 terminating decimal & 1 repeating decimal that are in between negative 1/2 and negative 1/3
-1/3 = 0.33333
-1/2 = 0.50
So, a repeating decimal in between could be
-0.3337777777...
-0.40404040404040...
-0.4444444...
-0.4988888888..
For a terminating, just delete the ...
-0.345
-0.432
and so on
can someone at least explain to me how to do this?
To find a terminating decimal and a repeating decimal between -1/2 and -1/3, we can convert these fractions into decimals and then explore the possible values.
Converting -1/2 to a decimal:
-1/2 = -0.5
Converting -1/3 to a decimal:
To convert -1/3 to a decimal, we perform long division:
-0.33333...
-3) 1.00000...
-0.99999...
Since the division repeats, we can represent -1/3 in decimal form as -0.3 with a repeating decimal of 3s: -0.3...
Now, let's find a terminating decimal between -0.5 and -0.3:
One possible option is -0.4, as it terminates and lies between -0.5 and -0.3.
Next, let's find a repeating decimal between -0.5 and -0.3:
One option is -0.43, where 3 is a repeating decimal.
Therefore, using the given conditions, we have:
-1/2 = -0.5
-1/3 ≈ -0.3...
A terminating decimal between -1/2 and -1/3 is -0.4, and a repeating decimal is -0.43.
To find terminating and repeating decimals between -1/2 and -1/3, we need to explore the decimal representations of these fractions.
Let's start with the fraction -1/2. To convert it into a decimal, you divide -1 by 2.
-1 ÷ 2 = -0.5
Therefore, -1/2 can be represented as -0.5 as a decimal. Since -0.5 is a terminating decimal (it ends after the digit 5), we have one terminating decimal between -1/2 and -1/3.
Now, let's move on to the fraction -1/3. To convert this into a decimal, you divide -1 by 3.
-1 ÷ 3 = -0.333...
The decimal -0.333... is a repeating decimal because it has a recurring decimal pattern (the digit 3 repeats indefinitely).
Now, to find a decimal between -0.5 and -0.333..., we can take the average of these two numbers:
(-0.5 + (-0.333...))/2 = -0.4165...
So, we have one terminating decimal (-0.5) and one repeating decimal (-0.4165...) between -1/2 and -1/3.