Final answer:
To find the smaller decimal from each pair, compare the digits from the highest value place to the right and choose the number with the smaller digit. Write numbers in scientific notation with a coefficient between 1 and 10 and an exponent to indicate the decimal movement. The process is similar when ordering decimal numbers by size or when applying inequality signs.
Step-by-step explanation:
To compare decimal numbers, look at the digits from left to right, starting with the highest value place (the leftmost digit) and moving to the right. When comparing, the number with the smaller digit in the first place where they differ is the smaller number. If we compare 13.5 and 9.99, the first digit where they differ is the tens place; since 9 is less than 13, 9.99 is the smaller number. This approach is applied to each pair to find the smaller number from each.
- The smaller decimal from each pair is: a) 9.99 b) 3.67 c) 12.56 d) 127.06 e) 0.67 f) 3.21 g) 18.45 h) 0.043 i) 0.09
- In order of size from smallest to largest: a) 2.6, 3.31, 3.46, 3.49 b) 0.52, 0.59, 0.71, 0.77 c) 6.8, 6.82, 6.9, 6.97 d) 5.199, 5.2, 5.212, 5.219 e) 32.4, 32.42, 32.441, 32.448 f) 9.03, 9.08, 9.7, 9.901, 9.99
- The correct signs between each pair of numbers are: a) < b) < c) < d) > e) > f) < g) > h) >
When writing numbers in scientific notation, make sure that the coefficient is between 1 and 10 and that the exponent on the 10 shows how many places the decimal is moved. For example, -8 in scientific notation would be -8.099 x 10³.