Write each rational number in the form a/b, where a and b are integers.
1. 0.3 2. 2 ⅞ 3. -5 4. 16
5. -1 ¾ 6. -4.5 7. 3 8. 0.11
0.3 = 3/10
2 7/8 = 16/8 + 7/8 = 23/8
and so on
-5
1. To write 0.3 as a fraction, we can set it up as follows:
0.3 = 3/10
2. To write 2 ⅞ as a fraction, we convert the mixed number to an improper fraction:
2 ⅞ = (2 * 8 + 7) / 8 = 23/8
3. The number -5 can be expressed as a fraction with a denominator of 1:
-5 = -5/1
4. The integer 16 can be written as a fraction with a denominator of 1:
16 = 16/1
5. To express -1 ¾ as a fraction, we convert the mixed number to an improper fraction:
-1 ¾ = (-1 * 4 + 3) / 4 = -7/4
6. The decimal -4.5 can be expressed as a fraction by placing it over a power of 10:
-4.5 = -45/10
7. The number 3 can be expressed as a fraction with a denominator of 1:
3 = 3/1
8. To write 0.11 as a fraction, we need to count the number of decimal places, which in this case is 2. We then place the decimal representation over 1 followed by the same number of zeros as there are decimal places:
0.11 = 11/100
To write each rational number in the form a/b where a and b are integers, we need to find a way to express the given numbers as fractions.
1. 0.3: To convert a decimal to a fraction, we place the decimal number over the place value it occupies. In this case, 0.3 is in the tenths place, so we can write it as 3/10.
2. 2 ⅞: To convert a mixed number to a fraction, we multiply the whole number by the denominator of the fraction and add the numerator. In this case, we have 2 multiplied by 8 (16) plus 7, which gives us 23. So, the fraction form of 2 ⅞ is 23/8.
3. -5: Since this number is already an integer, we can write it as -5/1.
4. 16: Similar to the previous case, we can write 16 as 16/1.
5. -1 ¾: Following the same approach for converting mixed numbers, we multiply -1 by 4 (giving us -4) and add 3, resulting in -1 ¾ as -7/4.
6. -4.5: To convert a decimal to a fraction, we place the decimal number over the place value it occupies. In this case, 4.5 is in the tenths place, so we can write it as -45/10. However, it's generally good practice to simplify fractions. By dividing both the numerator and denominator by 5, we get -9/2.
7. 3: We can write 3 as 3/1, which is already in fraction form.
8. 0.11: Similar to case 6, we can write 0.11 as 11/100. As a final step, we can simplify this fraction by dividing both the numerator and denominator by 11, which gives us 1/9.
So, the rational number forms of the given numbers are:
1. 0.3 = 3/10
2. 2 ⅞ = 23/8
3. -5 = -5/1
4. 16 = 16/1
5. -1 ¾ = -7/4
6. -4.5 = -9/2
7. 3 = 3/1
8. 0.11 = 1/9